1. Field of the Invention
The present invention relates to a method for obtaining an optimum model of a physical characteristic in a heterogeneous medium.
2. Description of the Prior Art
It is well-known at the present time that the precision and reliability of a reservoir model greatly depends on an integration of compatible data of different natures, connected with the properties of a reservoir which has been studied. Many surveys have for example shown the part that can be played by seismic data for constraining an image of a reservoir in the spaces contained between the wells drilled therein.
A common strategy for integrating seismic data into a reservoir model estimates the acoustic or elastic impedances from the seismic amplitudes and in translating the impedances into reservoir properties.
Among the inversion algorithms, the techniques using an a priori model require selection of parameters that weigh the respective influences of the data and of the a priori model in the optimization.
U.S. Pat. No. 4,972,383 and EP-889,331 filed by the assignee describe a method known as the Interwell(copyright) method which allows obtaining an at least two-dimensional model representing the acoustic impedance variations of an underground zone, which best matches known data deduced from observations or measurements: geologic data, post-stack seismic data, or other data obtained in one or more wells drilled through the zone, etc. The Interwell(copyright) method comprises construction of an a priori impedance model by combining well data and known structural or stratigraphic data, notably by kriging of the known impedances along the wells by following the correlation surfaces, inside stratigraphic units. The seismic horizons give the geometry of these stratigraphic units and correlations are performed by following the surfaces defined in accordance with the deposition mode (concordant, parallel to the roof or to the floor). The initial impedance distribution among the wells is then updated by taking account of the seismic amplitudes measured. This is achieved iteratively by minimizing a two-term cost function:
F=Fs+Fg, where:
Fs is a seismic term defined as a certain norm representative of the difference between the synthetic traces obtained from the model and the amplitudes of the real seismic traces: pre-stack traces, post-stack traces, etc., and
Fg is a geologic term measuring the difference between the a priori model and the standard model.
The optimum impedance model is a compromise between the two terms depending on the respective weights thereof. These weights are related to the inversion parameters, that is, for Fs, to the signal-to-noise ratio and, for Fg, to the correlation length xcex and the variance "sgr"2 of the error on the a priori model, assuming that this error is a random variable with a stationary exponential covariance of variance "sgr"2 and of correlation length xcex.
The weight of Fs is usually estimated from the real amplitudes. Conversely, correlation length xcex and standard deviation "sgr" are defined by the user according to the degree of confidence the user can have in the a priori model. However, this point should not be assessed too heuristically because the confidence the user can have in the a priori model depends on the quality of the data, on the number and location of the wells, and also on the spatial behavior of the impedance field.
The method according to the invention allows obtaining, by inversion, an optimized model of a physical quantity representative of a stratified heterogeneous medium (the impedance of this medium in relation to waves propagated therein for example), by means of a more quantitative characterization of inversion parameters (standard deviation and correlation length for example) that is consistent with the structure of the data observed or measured in the medium. By specifying the interdependence of these parameters, the method advantageously guides the interpreter in the selection of the values to be taken into account for the parameters. The resulting model is improved in relation to the model obtained by means of a purely heuristic selection.
The method according to the invention allows modelling the impedance of an underground zone in relation to waves propagated therein, and the obtaining of an image of the subsoil where the discontinuities generating these impedance variations are located more precisely. The invention has an application of facilitating location of hydrocarbon reservoirs.
The method comprises construction of an a priori model from known data obtained by measurements, recordings or observations at a number of points of the medium, and construction of an optimum model by iteratively minimizing a cost function depending on the differences between the model being sought and the known data, considering the a priori model.
The method of the invention constructs the a priori model, the construction comprising a correlation by kriging with a covariance (Cz) between the known values of the physical quantity at different points of the medium along discontinuities (strata directions), the uncertainties about the values of the physical quantity in the a priori model in relation to the corresponding values in the medium, at any point along these directions, following a covariance model (Cxcex5) that controls the inversion parameters, the model comprising a stationary covariance term (Cz) depending only on a distance vector ({right arrow over (h)}) between the points and a non-stationary covariance term depending on the position of the points and on the distances between one another respectively.
According to a first embodiment, a mean covariance ({overscore (C)}xcex5) is determined and adjusted to a stationary exponential covariance model (of a well-known type) in order to define the inversion parameters more precisely than with the conventional heuristic method.
According to a second embodiment, the covariance term (Cxcex5) is adjusted at all points to a stationary exponential model in order to obtain local values (xcexx, "sgr"x) of the inversion parameters.